Numerous designs of rotary internal combustion engines have been proposed which utilize a rotor which is effective to perform the compression and the power functions of the engine. The present invention is directed to this type of arrangement with there being provided an improved design which is of simple construction and efficient in its operation. The invention utilizes power members that move laterally outward and inward of the rotor to follow the inner peripheral wall of the stator, with these members having compression pockets into which a compressed gas charge is conveyed. These members are self-actuating through the effect of the compressed gas charge and as a result of centrifugal force. The compression function takes place through the action of vanes which cooperate with arcuately disposed recesses. These vanes and recesses are positioned on opposite sides of the rotor to provide for a balanced force on the rotor and for moving the compressed gas charge to the pockets or recesses of the laterally moving members from opposite sides of the same. With the arrangement of the invention the motion of gases with respect to their containing surfaces is limited to a low value with there being a minimal dead gas pocket and no extended gas passages.